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Curriculum Vitae Christian Haesemeyer Address: School of Mathematics & Statistics University of Melbourne Parkville, VIC 3010 web: http://blogs.unimelb.edu.au/christian-haesemeyer/ Education: Ph.D. in Mathematics, Northwestern University, June 2003 (advisors: Andrei A. • Suslin and Eric M. Friedlander, thesis title: Descent properties for homotopy K- theory) Diploma in Mathematics, Bonn University, 1999 • Employment: Professor, University of Melbourne, 2015- present. • Professor, University of California Los Angeles, 2014- 2015. • Assoc. Professor at the University of California Los Angeles, 2008-2014. • Asst. Professor (tenure track) at the University of Illinois at Chicago, 2007-2008 • Member, Institute for Advanced Study, 2004-2005. • J.L. Doob Assistant Professor at the University of Illinois, Urbana-Champaign, • 2003-2007. Papers and Preprints: On the topological period-index problem over 8-manifolds, with D. Crowley and • X. Gu. Preprint 2019. https://arxiv.org/abs/1911.07206 The K -theory of monoid sets, with C. Weibel. Preprint 2019. • ′ https://arxiv.org/abs/1909.00297. Submitted. K-theory of line bundles and smooth varieties, with C. Weibel. Proc. Amer. • Math. Soc. 146 (2018), 4139–4150. The K-theory of toric schemes over regular rings of mixed characteristic, with G. • Cortin˜as, M. E. Walker and C. Weibel. Singularities, algebraic geometry, commu- tative algebra, and related topics 455–479, Springer, Cham, 2018. The K-theory of toric varieties in positive characteristic, with G. Cortin˜as, M. E. • Walker and C. Weibel. Journal of Topology 7:247–286, 2014. The 0-th stable A1-homotopy sheaf and quadratic zero cycles, with A. Asok. • Preprint 2011. 1 Toric varieties, monoid schemes, and cdh descent, with G. Cortin˜as, M. E. Walker • and C. Weibel. Journal fu¨r die Reine und Angewandte Mathematik 698:1–54, 2015. Stable A1 homotopy and R-equivalence, with A. Asok. JPAA 215(10):2469–2472, • 2011. A negative answer to a question of Bass, with G. Cortin˜as, M. E. Walker and C. • Weibel. Proc. AMS 139(4):1187–1200, 2011. K-theory of cones of smooth varieties, with G. Cortin˜as, M. E. Walker and C. • Weibel. Journal of Alg. Geom. 22:13–34, 2013. Lipschitz cocycles and Poincare duality, with E. M. Friedlander. In: The geometry • of algebraic cycles. AMS, 2010. Norm varieties and the Chain Lemma (after Markus Rost), with C. Weibel. Abel • Symp. 4, Springer, Berlin 2009. Bass’ NK groups and cdh-fibrant Hochschild homology, with G. Cortin˜as, M. E. • Walker and C. Weibel. Inv. Math. 181:421–448, 2010. The K-theory of toric varieties, with G. Cortin˜as, M. E. Walker and C. Weibel. • Trans. AMS 361(6):3325–3341, 2009. Infinitesimal cohomology and the Chern character to negative cyclic homology, • with G. Cortin˜as and C. Weibel. Math. Ann. 344(4):891–922, 2009. K-regularity, cdh-fibrant Hochschild homology, and a conjecture of Vorst, with G. • Cortin˜as and C. Weibel. Journal of the AMS, 21(2):547–561, 2008. Cyclic homology, cdh-cohomology and negative K-theory, with G. Cortin˜as, M. • Schlichting and C. Weibel. Annals of Math. 167(2):549–573, 2008. Motives and ´etale motives with finite coefficients, with J. Hornbostel. K-Theory • 34(3):195–207, 2005. Descent properties of homotopy K-theory, Duke Math. J. 125(3):589-619 (2004). • Techniques, computations and conjectures for semitopological K-theory, with E. • M. Friedlander and M. E. Walker, Math. Ann. 330:759-807 (2004). Monograph: The Norm residue Theorem in Motivic Cohomology, 299 + xiii pages, with C. • Weibel. Annals of Mathematics Studies 200, Princeton University Press 2019. Presentations (Conferences): K-theory and Motives, workshop at Newton Institute Cambridge, March 2020 - • cancelled Motives in Tokyo 2018, on the occasion of Shuji Saito’s 60th birthday, March 2018. • The 60th birthday of Amnon Neeman, conference, ANU September 2017. • 2 Workshop on Motives, Tokyo, February 2017. • Workshop on Motives, Tokyo, February 2016. • International Colloquium on K-theory, Tata Institute for Fundamental Research, • Mumbai, January 2016. Homotopical Algebra Summer Days, IMUB Bracelona, July 2014. • Representation Theory and K-theory, Los Angeles, May 2014. • Session on Contemporary trends in algebraic geometry and K-theory, at the Math- • ematical Congress of the Americas, Guanajato Mexico, August 2013. Workshop on Torsors, motives, and cohomological invariants, Fields Institute • Toronto, Canada, May 2013. Conference on Algebraic K-theory and Arithmetic, Bedlewo (Poland), July 2012. • Workshop on Motives, Tokyo, December 2011. • Workshop on Geometric Aspects of Motivic Homotopy Theory, Bonn (Germany), • September 2010. Workshop on Motivic Homotopy Theory, Muenster (Germany), July 2009. • Western Algebraic Geometry Seminar, MSRI Berkeley (CA), April 2009. • Conference on Homotopy Theory and Applications, Lincoln (NE), March 2009. • Workshop on Motives, Tokyo, December 2008. • Midwest topology meeting, Evanston (IL), May 2008. • Conference on Algebraic Cycles, Columbus (OH), March 2008. • Meeting on Algebraic K-theory, Oberwolfach, July 2006. • Great Lakes K-theory Conference XI, Chicago, April 2006. • Conference on Algebraic K-theory and its Applications, Safi, Morocco, July 2004. • Workshop on Motivic Homotopy Theory, IHP Paris, May 2004. • Great Lakes K-theory Conference X, Urbana-Champaign, May 2004. • Meeting on Algebraic K-theory, Oberwolfach, August 2002. • Presentations (Seminars and Colloquia): Algebra Seminar, UCLA, January 2019. • Colloquium, Universit¨at Osnabru´ck, June 2017. • Geometry & Topology Seminar, University of Sydney, June 2016. • Algebra & Topology Seminar, Australian National University, Canberra, October • 2015. 3 Topology Seminar, University of Minnesota, January 2015 • Algebra and Topology Seminar, Melbourne University, October 2013. • Topology Seminar, MIT, September 2013. • Topology Seminar, University of Western Ontario, September 2013. • Algebra Seminar, University of Washington, May 2013. • Colloquium, California State University Fullerton, April 2013. • Topology Seminar, Stanford University, April 2013. • Topology Seminar, University of Wuppertal (Germany), November 2012. • Colloquium, University of Hamburg (Germany), November 2012. • Algebra Seminar, Warwick University, October 2012. • Colloquium and Algebra Seminar, University of Heidelberg (Germany), October • 2012. Colloquium, University of California at Riverside, April 2012. • Topology Seminar, University of Oregon, April 2012. • Algebra Seminar, University of Nebraska in Lincoln, October 2011. • Colloquium, New Mexico State University, September 2011. • Algebra Seminar, Rutgers University, February 2011. • Algebra/Topology Seminar, University of Western Ontario, November 2010. • Colloquium, University of Illinois at Chicago, February 2008. • Algebra Seminar and Colloquium, USC, October 2007. • Algebra Seminar, UCLA, May 2006. • Algebra Seminar, Northwestern University, February 2006. • Topology Seminar, UIUC, fall 2005. • Algebra, Geometry and Physics Seminar, Stony Brook University-SUNY, July • 2005. K-theory Seminar, Ohio State University, April 2005. • Joint Algebra/Topology Seminar, University of Oregon, March 2005. • Algebra Seminar, Rutgers University, February 2005. • Geometry-Algebra-Singularities-Combinatorics Seminar, Northeastern University, • November 2004. Topology Seminar, UIUC, fall 2003. • 4 Essen University, June 2003. • Motivic Cohomology Seminar, University of Illinois at Urbana-Champaign, Novem- • ber 2002. Algebra Seminar, Northwestern University, November 2002. • Topology Seminar, University of Heidelberg, July 2001. • Grants and Awards: ARC Discovery Project DP170102328, 2017-2019. Award amount $ 345,000. • NSF Focused Research Group DMS-0966821, 2010-2014. Collaborative grant with • Mark E. Walker (University of Nebraska), Charles Weibel (Rutgers University) and Eric Friedlander and Aravind Asok (University of Southern California). The total amount awarded was $ 2.1 million. The amount awarded to UCLA is US $ 361,835. NSF grant DMS-0652860, 2007-2011. Award amount US $ 95,114. • Clay Math Institute Liftoff Fellowship, Summer 2003. • Professional Activities: I served as guest editor for two special issues of the Journal of Pure and Applied Algebra: in honour of Eric Friedlander’s 60th birthday (2005) and in honour of Charles Weibel’s 65th birthday (2017). I have refereed, among other journals, for Annals of Math., Journal of the AMS, Inv. Math., Acta Math., Trans. AMS, Compositio Math., American Journal of Math., Duke Math. J., Math. Ann., Geometry & Topology, Journal of Pure and Applied Algebra. I have been a reviewer for MathSciNet. I have been a reviewer for the ARC. I co-organized the following conferences and seminars: International Conference in K-theory, Western Sydney University, August 2016. • K-theory, cyclic homology and motives - a conference in celebration of C. A. • Weibel’s 65th year., Rutgers University, New Brunswick NJ, August 2015. Conference on Homotopical Methods in Algebraic Geometry, University of South- • ern California, Los Angeles, 2013. Workshop on New Directions in Algebraic K-theory, Mathematisches Forschungsin- • stitut Oberwolfach (Germany) 2011. Conference on K-theory and Motives, on the occasion of the 60th birthday of • Andrei Suslin, Los Angeles (CA) 2011. Southern California Algebraic Geometry Seminar, Los Angeles (CA) 2010, 2011, • 2014 San Diego (CA) 2011, 2012, 2013, 2014. Session on Homotopy Theory and K-theory, AMS sectional meeting, Los Angeles • (CA) 2010. 5 Session on Algebraic K-theory and Nil groups in algebra and topology,
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    References [1] V. A. Voevodski˘ı. Galois group Gal(Q¯ =Q) and Teihmuller modular groups. In Proc. Conf. Constr. Methods and Alg. Number Theory, Minsk, 1989. [2] V. A. Voevodski˘ıand G. B. Shabat. Equilateral triangulations of Riemann surfaces, and curves over algebraic number fields. Dokl. Akad. Nauk SSSR, 304(2):265{268, 1989. [3] G. B. Shabat and V. A. Voevodsky. Drawing curves over number fields. In The Grothendieck Festschrift, Vol. III, volume 88 of Progr. Math., pages 199{227. Birkh¨auser Boston, Boston, MA, 1990. [4] V. A. Voevodski˘ı. Etale´ topologies of schemes over fields of finite type over Q. Izv. Akad. Nauk SSSR Ser. Mat., 54(6):1155{1167, 1990. [5] V. A. Voevodski˘ı. Flags and Grothendieck cartographical group in higher dimensions. CSTARCI Math. Preprints, (05-90), 1990. [6] V. A. Voevodski˘ı.Triangulations of oriented manifolds and ramified coverings of sphere (in Russian). In Proc. Conf. of Young Scientists. Moscow Univ. Press, 1990. [7] V. A. Voevodski˘ı and M. M. Kapranov. 1-groupoids as a model for a homotopy category. Uspekhi Mat. Nauk, 45(5(275)):183{184, 1990. [8] V. A. Voevodski˘ıand M. M. Kapranov. Multidimensional categories (in Russian). In Proc. Conf. of Young Scientists. Moscow Univ. Press, 1990. [9] V. A. Voevodski˘ıand G. B. Shabat. Piece-wise euclidean approximation of Jacobians of algebraic curves. CSTARCI Math. Preprints, (01-90), 1990. [10] M. M. Kapranov and V. A. Voevodsky. Combinatorial-geometric aspects of polycategory theory: pasting schemes and higher Bruhat orders (list of results). Cahiers Topologie G´eom.Diff´erentielle Cat´eg., 32(1):11{27, 1991.
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  • Emissary | Spring 2021

    Emissary | Spring 2021

    Spring 2021 EMISSARY M a t h e m a t i c a lSc i e n c e sRe s e a r c hIn s t i t u t e www.msri.org Mathematical Problems in Fluid Dynamics Mihaela Ifrim, Daniel Tataru, and Igor Kukavica The exploration of the mathematical foundations of fluid dynamics began early on in human history. The study of the behavior of fluids dates back to Archimedes, who discovered that any body immersed in a liquid receives a vertical upward thrust, which is equal to the weight of the displaced liquid. Later, Leonardo Da Vinci was fascinated by turbulence, another key feature of fluid flows. But the first advances in the analysis of fluids date from the beginning of the eighteenth century with the birth of differential calculus, which revolutionized the mathematical understanding of the movement of bodies, solids, and fluids. The discovery of the governing equations for the motion of fluids goes back to Euler in 1757; further progress in the nineteenth century was due to Navier and later Stokes, who explored the role of viscosity. In the middle of the twenti- eth century, Kolmogorov’s theory of tur- bulence was another turning point, as it set future directions in the exploration of fluids. More complex geophysical models incorporating temperature, salinity, and ro- tation appeared subsequently, and they play a role in weather prediction and climate modeling. Nowadays, the field of mathematical fluid dynamics is one of the key areas of partial differential equations and has been the fo- cus of extensive research over the years.